For many, superstition is the last resort of the desperate and deluded but Dundee United must have hoped that the cameo appearance of a black cat scampering across the Tynecastle turf in the opening period of this game would prove a lucky omen.

But even good fortune appears to have jumped ship, – probably disheartened by the lack of hope and any other commodity which could prove useful in what is looking like and increasingly forlorn battle to avoid relegation.

In a match which threw up incident and goals, with two penalties, a red card and a final tally of five goals, the home side showed their superiority, preying on the obvious vulnerabilities of their guests.

The result moved Hearts a further three points clear of those keen to deny them a top-three berth and left United manager Mixu Paatelainen with more injury and suspension woes to add to all the other problems under which he is labouring.

A picture of frustration, anger and bewilderment, the Finn patrolled his technical area with the demented air of a man who thought he had signed up purgatory but found himself in hell.

Losing games is one thing but seeing his players gift them to the opposition is something much less palatable and the Tannadice side are turning that into an art form this season.

Such silliness was evident from the first thirty seconds of the match, when Michal Szromnik took a needless and all-too casual meander out of his box to attempt to deal with a loose ball and succeeded only in offering Osman Sow the chance to run at an empty goal before Callum Morris got across to clear.

From there United broke upfield and actually took the lead after left back Juwon Oshaniwa brought down Scott Fraser in the penalty area and conceded a spot kick which Billy Mckay converted.

But there was little likelihood of United making it through the remaining 89 minutes without conceding a goal. In fact, shambolic defending meant that, by the time the game had reached the 30th minute, the home side had turned matters on their head and moved into a commanding 3-1 lead.

That Hearts didn’t go on to pile on the misery and more goals will be a cause for consternation to the Tynecastle coaching staff, and that inability to cash in on their dominance threatened to undo Hearts in the closing minutes as 10-man United attempted to salvage only their third point on league duty since October.

Hearts had levelled things in the 18th minute when Gavin Reilly netted his third goal of the season after a corner from Sam Nicholson had been flicked on.

With some quick movement and link up play, they were torturing their guests at that stage of the game and in the 26th minute Hearts added a second to take a lead they would never relinquish. United made a mess of dealing with some sustained pressure and unable to clear their area sufficiently they were punished when Morgaro Gomis played the ball to Nicholson, who burst inside and joined up with Prince Buaben. Offering a angle as he charged into the box, the winger demanded a quick one-two but the former Tannadice midfielder opted to take on the shot himself and, from about 20 yards out, beat Szromnik. The keeper did get both hands to the ball but was pitifully inept when it came to preventing its ongoing passage into the net. The third goals came from the spot after Morris brought down King and Osman Sow netted for the 10th time this season.

But United showed some spirit, even if it was short-lived. A free-kick saw Fraser pull one back in the 44th minute but, within the space of a couple of minutes, Morris was carried off after he turned awkwardly trying to keep tabs on Reilly and the Hearts striker was felled by Mark Durnan, earning Hearts a free-kick and the defender a red card.

With only 10 men, the away side simply piled everyone behind the ball, offering a more stodgy defence. Hearts tried to penetrate it and they had their chances but they were not clinical enough, which made for an edgy final few minutes as United tried to grab an equaliser.

After five games without a victory, though, they managed to see the game out and win for the first time since the beginning of November. It offers the Tynecastle side plenty of positives to build from in the New Year. For United there is little to offer them joy.